A027769 a(n) = (n+1)*binomial(n+1, 9).

9, 100, 605, 2640, 9295, 28028, 75075, 183040, 413270, 875160, 1755182, 3359200, 6172530, 10943240, 18795370, 31380096, 51074375, 81238300, 126544275, 193393200, 290435145, 429214500, 624962325, 897561600, 1272714300, 1783342704, 2471261100, 3389158080

Offset: 8

Author

Thi Ngoc Dinh (via R. K. Guy)

Keywords

• nonn

Comments

Number of 11-subsequences of [ 1, n ] with just 1 contiguous pair.

13208*a(n) is the number of permutations of (n+1) symbols that 9-commute with an (n+1)-cycle (see A233440 for definition), where 13208=A000757(9). - Luis Manuel Rivera Martínez, Feb 06 2014

Links

• T. D. Noe, Table of n, a(n) for n = 8..1000
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Cf. A000757, A233440.

Programs

Mathematica

Table[(n+1)*Binomial[n+1, 9], {n, 8, 35}] (* Amiram Eldar, Jan 30 2022 *)

Formula

G.f.: (9+x)*x^8/(1-x)^11.

From Amiram Eldar, Jan 30 2022: (Start)

Sum_{n>=8} 1/a(n) = 3*Pi^2/2 - 575499/39200.

Sum_{n>=8} (-1)^n/a(n) = 3*Pi^2/4 + 24576*log(2)/35 - 19365109/39200. (End)